Effective decorrelation and space dimensionality reduction of multiscaling volatility

We consider an approach for modeling non-stationary and non-Gaussian curves which has a natural impact on financial time series analysis due to the characteristic features of volatility processes. Provided that one can approximate the signal of interest, in this case stock index returns, with a greedy approximation scheme based on wavelet-like functions, an effective space dimensionality reduction of the problem can be found by a decomposition technique which selects the scales according to an energy-based optimization scheme and finds the most informative sources of the underlying multiscaling volatility process.